MixLaw — Mixture distributions in R

An R package implementing an S3 class for probability distribution mixtures, with dedicated methods for random sampling, density visualization, and basic descriptive statistics. Includes a specialized subclass for mixtures of normal distributions.

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Overview

MixLaw provides an S3 framework to represent and manipulate mixtures of probability distributions in R. A mixture distribution is a weighted combination of several component distributions, widely used in statistical modeling for capturing heterogeneous populations, latent subgroups, or multi-modal phenomena.

The package exposes:

• A general-purpose S3 class melange_dist that accepts any list of one-argument random-number generators (e.g. rnorm, rexp, rgamma) along with a vector of mixture weights.
• A specialized subclass melange_normal for mixtures of normal distributions, parameterized directly by component means, standard deviations, and weights.
• Dedicated methods for the most common operations: random sampling, density plotting, descriptive statistics, and printing.

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Academic context

This package was developed as part of MAT8186 — Techniques avancées en programmation statistique : R, a graduate course at Université du Québec à Montréal (UQAM). The objective was to design and document a fully structured R package, demonstrating object-oriented programming through S3 dispatch, formal documentation with roxygen2, and unit testing with testthat.

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Features

• S3 class hierarchy with parent class melange_dist and specialized subclass melange_normal.
• Random sampling of mixture realizations via an S3-dispatched rand() generic.
• Density visualization through a custom plot() method.
• Descriptive statistics: mean() and quantile() methods on mixture realizations.
• Informative printing with a tabular summary of components and weights.
• Unit tests via testthat (edition 3).
• Full roxygen2 documentation with executable examples on every function.

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⚙️ Installation

The package is hosted on GitHub and can be installed directly using devtools:

# Install devtools if needed
install.packages("devtools")

# Install MixLaw from GitHub
devtools::install_github("komiayi/MixLaw")

# Load the package
library(MixLaw)

# Open the package help index
?MixLaw

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Usage

General mixture of arbitrary distributions

library(MixLaw)

# Build a mixture of three components: normal, exponential, and Gamma(shape=10)
M <- melange_dist(
  list(rnorm, rexp, \(n) rgamma(n, 10)),
  c(0.1, 0.2, 0.7)
)

# Inspect the object
print(M)

# Generate 100 realizations
sample_M <- rand(M, n = 100)

# Compute the empirical mean and quantiles
mean(M)
quantile(M, probs = c(0.25, 0.5, 0.75))

# Plot the empirical density
plot(M, color = "red", main = "Mixture density")

Mixture of normal distributions

# Mixture of two normals: N(1, 0.1²) and N(0.2, 0.8²), equal weights by default
N <- melange_normal(moy = c(1, 0.2), ect = c(0.1, 0.8))

# Inspect the components
print(N)

# Sample, summarize, and plot
mean(N)
quantile(N)
plot(N, main = "Normal mixture density")

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Repository structure

MixLaw/
├── R/                     # Source code of the S3 class and its methods
│   ├── melange_dist.R         # Constructor of the parent S3 class
│   ├── melange_normal.R       # Specialized subclass for normal mixtures
│   ├── rand_mellange_dist.R   # rand() S3 generic and method
│   ├── plot_melange_dist.R    # plot() method
│   ├── print_melange_dist.R   # print() method
│   ├── mean_melange_dist.R    # mean() method
│   ├── quantile_melange_dist.R # quantile() method
│   └── MixLaw-package.R       # Package-level documentation
├── man/                   # Generated Rd documentation (roxygen2 output)
├── tests/                 # Unit tests (testthat, edition 3)
├── DESCRIPTION            # Package metadata
├── NAMESPACE              # Exports and imports
├── .Rbuildignore
└── README.md

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Methods reference

Generic	Class	Purpose
melange_dist()	constructor	Build a mixture from a list of RNG functions and weights
melange_normal()	constructor	Build a normal mixture from means, standard deviations, weights
rand()	S3 generic	Sample n realizations from a mixture
print()	S3 method	Tabular summary of components and weights
plot()	S3 method	Empirical density plot of mixture realizations
mean()	S3 method	Empirical mean of realizations
quantile()	S3 method	Empirical quantiles of realizations

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Concepts demonstrated

The package was designed as a complete exercise in modern R package authoring. It illustrates:

• S3 object orientation, including class inheritance via vectorized class attributes (class = c("melange_normal", "melange_dist")) and method dispatch through UseMethod.
• Custom S3 generics (rand) alongside extensions of base R generics (print, plot, mean, quantile).
• Defensive programming with explicit input validation and informative error messages.
• roxygen2 documentation with @param, @return, @examples, and selective imports via @importFrom and @import.
• Unit testing under the testthat framework (edition 3).
• CRAN-style package layout, including DESCRIPTION, NAMESPACE, R/, man/, tests/, and .Rbuildignore.

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License

Distributed under the GNU General Public License v2.0 (GPL-2). See the LICENSE terms for full details.

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Author

Komi Roger Ayi Biostatistician — Data Scientist Université du Québec à Montréal · Montréal, Québec, Canada

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